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This proceedings volume originates from a conference held in Herrnhut in June 2013. It provides unique insights into the power of abstract methods and techniques in dealing successfully with numerous applications stemming from classical analysis and mathematical physics. The book features diverse topics in the area of operator semigroups, including partial differential equations, martingale and Hilbert transforms, Banach and von Neumann algebras, Schrödinger operators, maximal regularity and Fourier multipliers, interpolation, operator-theoretical problems (concerning generation, perturbation and dilation, for example), and various qualitative and quantitative Tauberian theorems with a focus on transfinite induction and magics of Cantor.
The last fifteen years have seen the dawn of a new era for semigroup theory with the emphasis on applications of abstract results, often unexpected and far removed from traditional ones. The aim of the conference was to bring together prominent experts in the field of modern semigroup theory, harmonic analysis, complex analysis and mathematical physics, and to present the lively interactions between all of those areas and beyond. In addition, the meeting honored the sixtieth anniversary of Prof C. J. K. Batty, whose scientific achievements are an impressive illustration of the conference goal. These proceedings present contributions by prominent scientists at this international conference, which became a landmark event.
They will be a valuable and inspiring source of information for graduate students and established researchers.
Front Matter
Polynomial Internal and External Stability of Well-posed Linear Systems
Countable Spectrum, Transfinite Induction and Stability
Maximal Regularity in Interpolation Spaces for Second-order Cauchy Problems
Stability of Quantum Dynamical Semigroups
Families of Operators Describing Diffusion Through Permeable Membranes
Multiscale Unique Continuation Properties of Eigenfunctions
Dichotomy Results for Norm Estimates in Operator Semigroups
Estimates on Non-uniform Stability for Bounded Semigroups
Convergence of the Dirichlet-to-Neumann Operator on Varying Domains
A Banach Algebra Approach to the Weak Spectral Mapping Theorem for Locally Compact Abelian Groups
Regularity Properties of Sectorial Operators: Counterexamples and Open Problems
Global Existence Results for the Navier–Stokes Equations in the Rotational Framework in Fourier–Besov Spaces
Some Operator Bounds Employing Complex Interpolation Revisited
Generation of Subordinated Holomorphic Semigroups via Yosida’s Theorem
A Quantitative Coulhon–Lamberton Theorem
An Analytic Family of Contractions Generated by the Volterra Operator
Lattice Dilations of Bistochastic Semigroups
Domains of Fractional Powers of Matrix-valued Operators: A General Approach
General Mazur–Ulam Type Theorems and Some Applications
Traces of Non-regular Vector Fields on Lipschitz Domains
A Murray–von Neumann Type Classification of C*-algebras
Well-posedness viaMonotonicity – an Overview
Perturbations of Exponential Dichotomies for Hyperbolic Evolution Equations
Gaussian and non-Gaussian Behaviour of Diffusion Processes
On Self-adjoint Extensions of Symmetric Operators